VM is calling force-mode-line-update in a Folder buffer, which is
generally invisible. The function is updating its menubar, but not that
of the currently visible buffer. Even after I change it the way I
mentioned in my previous post, it still doesn't work because the
"other-buffer" also turns out to be the Folder buffer for some reason or
the other.

I gets better: `(set-buffer-modified-p (buffer-modified-p))'
apparently does nothing, because it sets the buffer's modified flag to
the same value it has already. So this function actually does nothing
at all, right?

That would be logical, but I am guessing from force-mode-line-update's
doc string that this has the effect of updating the mode line, menu bar
and the rest.

It is a pity that set-buffer-modified-p's doc string doesn't do justice
to all that it does!